The sum of two numbers is $129$, and their difference is $1$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 129}$ ${x-y = 1}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 130 $ $ x = \dfrac{130}{2} $ ${x = 65}$ Now that you know ${x = 65}$ , plug it back into $ {x+y = 129}$ to find $y$ ${(65)}{ + y = 129}$ ${y = 64}$ You can also plug ${x = 65}$ into $ {x-y = 1}$ and get the same answer for $y$ ${(65)}{ - y = 1}$ ${y = 64}$ Therefore, the larger number is $65$, and the smaller number is $64$.